Apply the apparent power limit at both ends in bus injection solved as a non-linear program

[erikfilias]

Problem

IndACApparentPowerLimit limits the apparent power at both ends of each AC branch to its rating. It was read for every AC formulation but applied only in branch flow (IndACPowerFlow = 1). In bus injection (IndACPowerFlow = 2 and 3), the far end of a branch had no apparent power limit, and the near end only eBIMSLimit, the counterpart of the current limit, which admits up to the rating times V/Vmin. A case could turn the option on in bus injection and get branches above their rating, with no message.

Observed behaviour

9n_AC, first 12 hours, option on in every row:

	Largest loading	Branch-hours above the rating	Generation cost
Rectangular coordinates, before	105.03 %	6	0.209405 MEUR
Branch flow with the AC recovery step	99.60 %	0	0.230587 MEUR

Solution

The constraints move from the branch flow block into one function, _ApparentPowerLimit, used by both formulations; both name their far-end flows vFlowElecBck and vFlowReactBck. Bus injection applies them as the circle where the model is solved as a non-linear program anyway: rectangular coordinates, W space with the loop condition (IndACCycle = 1), and IndACModelType = 2.

In the W-space cone solved with Gurobi, the option is not applied, and a warning says so. There the inscribed polygon made Gurobi's barrier stop with numerical trouble on 9n_AC after five iterations, although ipopt solved the same model with every branch within its rating, and BarHomogeneous = 1 did not help.

After the change

The same case:

	Largest loading	Branch-hours above the rating	Generation cost
Rectangular coordinates, after	99.77 %	0	0.228961 MEUR

Notes

• Branch flow is unchanged. On a 695-bus Nordic case, one hour in branch flow with the recovery step gives the same cost (2.4420 -> 2.5503 MEUR) and the same nodal prices to four decimals before and after.
• On that Nordic case with the thinner conductor bundle, rectangular coordinates priced SE4 at 127.0 EUR/MWh at the evening peak without the limit and 226.6 with it, the value branch flow with the recovery step gives. Over a day solved hour by hour, rectangular coordinates now reach the branch flow optimum to four decimals (53.2777 against 53.2776 MEUR) in about a sixth of the solve time.
• Three tests: the limit holds in rectangular coordinates and in W space with the loop condition on 9n_AC, and the W-space cone reports that it is not applied. tests/test_ac_input.py and tests/test_ac_hvdc_and_setpoints.py pass (112).
• The CHANGELOG has an entry under 4.19.0rc.
• The branch carries master as of 9 October (merge commit 8dca104). The one conflict was the option comment in
  openTEPES_InputData.py, where master added the IndACRestoreWarmStart line; both lines are kept. The two modules
  changed here are dated October 09, 2026. tests/test_ac_input.py and tests/test_ac_hvdc_and_setpoints.py pass on
  the merged tree (114).